WO2018223285A1 - 波束-多普勒方向图稀疏约束的stap方法及装置 - Google Patents

波束-多普勒方向图稀疏约束的stap方法及装置 Download PDF

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WO2018223285A1
WO2018223285A1 PCT/CN2017/087289 CN2017087289W WO2018223285A1 WO 2018223285 A1 WO2018223285 A1 WO 2018223285A1 CN 2017087289 W CN2017087289 W CN 2017087289W WO 2018223285 A1 WO2018223285 A1 WO 2018223285A1
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norm
space
time
doppler
weight vector
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French (fr)
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阳召成
汪小叶
朱轶昂
黄建军
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深圳大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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  • the invention belongs to the field of radar signal processing, and in particular relates to a STAP method and device for beam-Doppler pattern sparse constraint.
  • STAP Space-Time Adaptive Processing
  • reduced Dimension STAP methods such as Joint Domain Localized (JDL)
  • Reduced Rank STAP methods such as principal component method). Principle Components, PC
  • STAP method based on model parameterization
  • KA Knowledge-Aided
  • STAP method sparse space-time beamforming method based on weight vector sparsity
  • minimum-maximum STAP method and so on.
  • the reduced-dimensional STAP method uses the method of reducing the degree of freedom of the system to improve the clutter suppression ability and target detection performance under the limited and identical distributed training samples, but the algorithm reduces the degree of system freedom, compared with the optimal system under the full-space time. Clutter suppression Performance is reduced.
  • the reduced rank STAP method can obtain better performance than the dimension-reduced STAP method, although the filter weight vector can be designed according to environmental changes and sample data in real time.
  • the performance of the reduced rank STAP method usually depends on the actual clutter environment.
  • the accuracy of the mid-fuzzy rank estimation, and the accuracy of the estimation of the clutter rank in the actual clutter environment still needs more research.
  • the STAP method based on model parameterization solves the problem of finitely independent and identically distributed training samples by using the model parameter method.
  • the computational complexity of this method is high, and the performance of the algorithm depends on the rationality of model parameter selection.
  • the knowledge-based STAP method has great advantages in solving the problem of limited number of independent and identically distributed training samples, but the performance of this method depends on the accuracy of knowledge.
  • the sparse space-time beamforming method based on weight vector sparsity utilizes the prior knowledge of weight vector sparsity. It has potential advantages when the independent and identical distribution training is limited, but its clutter performance is reduced when there is model mismatch.
  • the min-max STAP method uses the iterative min-max method to select the antenna pulse pair to reduce the need for space-time snapshots, so it can achieve better clutter suppression with limited snapshots, but the iterations involved in the algorithm are minimal-maximum
  • the computational complexity of the process is high, and the performance of the algorithm deteriorates severely when the antenna pair is not properly selected.
  • the invention provides a beam-Doppler pattern sparse constraint STAP method and device, aiming at providing an easy-to-set parameter and simple calculation algorithm to improve the traditional space time under the condition that the number of independent and identically distributed training samples is limited.
  • the adaptive filter 's clutter suppression level and target detection capability.
  • the present invention provides a space-time adaptive processing STAP method for beam-Doppler pattern sparse constraint, the method comprising:
  • the superscript p represents the number of independent and identically distributed training samples, and p is a positive integer.
  • L1 norm-L2 norm mixture minimization objective function is:
  • w p represents the weight vector of the NM ⁇ 1 -dimensional space-time filter calculated by p space-time snapshots
  • J 1 (w p ) represents a function with w p as a variable
  • R p w p represents the l 2 norm of the space-time filter output calculated by p space-time snapshots
  • R p represents the array covariance matrix calculated from p space-time snapshots, ⁇
  • the p 1 space-time snapshot is calculated by the beam-Doppler pattern z p l 1 sparse constraint term,
  • the beam-Doppler pattern representing the beam-Doppler space, the superscripts T and H respectively represent transposition and conjugate transposition, a beam-Doppler pattern representing a Doppler frequency of f d;i , a spatial frequency of f s;j , NM ⁇ N d N s
  • NM ⁇ 1 dimensional space-time snapshot is expressed as:
  • M represents the number of array elements of the antenna array
  • N represents the number of coherent pulses
  • ⁇ t is the target complex gain
  • Spatial frequency is The space-time steering vector corresponding to the target
  • x u includes a vector of clutter x c , interference x j , and noise x n .
  • the solving the weight vector w p of the space-time filter according to the L1 norm-L2 norm hybrid minimization objective function comprises:
  • ⁇ is the Lagrangian multiplier, Indicates that the number in the braces is the real part
  • ⁇ is the forgetting factor
  • x i is the ith space-time snapshot
  • x p is the p-th space-time snapshot
  • the superscript H is the conjugate transpose
  • R p-1 is the pre-p-1 space.
  • ⁇ p (z p ) represents the regularization parameter ⁇ calculated from p space-time snapshots, Is a constant, and
  • the present invention also provides a space-time adaptive processing STAP apparatus for beam-Doppler pattern sparse constraint, the apparatus comprising:
  • Minimizing the objective function building module for establishing the sparsity of the beam-Doppler pattern combining the l 2 norm of the space-time filter output and the minimization of the l 1 norm of the beam-Doppler pattern L1 norm-L2 norm mixing minimizes the objective function;
  • Weight vector w p solver module according to the L1 norm norm -L2 mixing minimize the objective function filter weight vector w p solving space-time;
  • the superscript p represents the number of independent and identically distributed training samples, and p is a positive integer.
  • L1 norm-L2 norm mixture minimization objective function is:
  • w p represents the weight vector of the NM ⁇ 1 -dimensional space-time filter calculated by p space-time snapshots
  • J 1 (w p ) represents a function with w p as a variable
  • R p w p represents the l 2 norm of the space-time filter output calculated by p space-time snapshots
  • R p represents the array covariance matrix calculated from p space-time snapshots, ⁇
  • the p 1 space-time snapshot is calculated by the beam-Doppler pattern z p l 1 sparse constraint term,
  • the beam-Doppler pattern representing the beam-Doppler space, the superscripts T and H respectively represent transposition and conjugate transposition, a beam-Doppler pattern representing a Doppler frequency of f d;i , a spatial frequency of f s;j , NM ⁇ N d N s
  • NM ⁇ 1 dimensional space-time snapshot is expressed as:
  • M represents the number of array elements of the antenna array
  • N represents the number of coherent pulses
  • ⁇ t is the target re-enhancement
  • Spatial frequency is The space-time steering vector corresponding to the target
  • x u includes a vector of clutter x c , interference x j , and noise x n .
  • weight vector w p solving module is specifically configured to convert the L1 norm-L2 norm mixture minimization objective function into the following formula:
  • ⁇ is the Lagrangian multiplier, Indicates that the number in the braces is the real part
  • ⁇ is the forgetting factor
  • x i is the ith space-time snapshot
  • x p is the p-th space-time snapshot
  • the superscript H is the conjugate transpose
  • R p-1 is the pre-p-1 space.
  • ⁇ p (z p ) represents the regularization parameter ⁇ calculated from p space-time snapshots, Is a constant, and
  • the present invention has the beneficial effects that the STAP method and device for beam-Doppler pattern sparse constraint provided by the present invention pass the traditional in the case that the number of independent and identically distributed training samples is p.
  • the weight vector w p of the time filter solves the above-mentioned minimization optimization problem; the method parameters provided by the invention are easy to set and simple to calculate, and the radar system suppression level can be improved under the condition that the number of independent and identically distributed training samples is limited.
  • FIG. 1 is a schematic flowchart of a space-time adaptive STAP method for beam-Doppler pattern sparse constraint according to an embodiment of the present invention
  • FIG. 2 is a schematic diagram of a relationship between a SINR loss and a training sample number according to an embodiment of the present invention
  • FIG. 3 is a schematic diagram of a relationship between a SINR loss and a target Doppler frequency according to an embodiment of the present invention
  • SNR signal-to-noise ratio
  • FIG. 5 is a schematic block diagram of a space-time adaptive processing STAP apparatus for beam-Doppler pattern sparse constraint according to an embodiment of the present invention.
  • the main implementation idea of the present invention is: when the number of independent and identically distributed training samples is p, the STAP filter design problem is described by introducing the sparsity of the beam-multiple map on the basis of the traditional STAP filter design.
  • L1 -L2 is the norm norm minimization mixing optimization problem, l joint space-time filter output and beam norm - Doppler pattern of minimizing l 1 norm, to establish the norm L1 norm -L2
  • the minimization of the objective function is mixed, and the weight vector w p of the space-time filter is solved according to the L1 norm-L2 norm hybrid minimization objective function, thereby solving the above minimization optimization problem.
  • the space-time adaptive processing STAP method of the beam-Doppler pattern sparse constraint is specifically described below. As shown in FIG. 1, the method includes:
  • Step S1 the beam according to - l sparse pattern of Doppler, the joint air filter output norm and beam - l Doppler direction in FIG. 1 is minimized norm established norm L1 norm -L2 Number mixing minimizes the objective function;
  • the sparseness of the beam-Doppler direction means that the beam-Doppler pattern forms a high gain in the target direction, and forms a very small gain in other directions than the target direction, that is, most components in a vector. The value is small, and only a few components have larger values, that is, the signal is sparse.
  • the number of space-time snapshots is p (p is a positive integer)
  • the beam-Doppler pattern formed by the space-time filter weight vector is used. Sparseness, combined with space-time filter output power (the mathematical significance of the space-time filter output power is the l 2 norm) and the beam-Doppler pattern's l 1 norm is minimized, resulting in a target optimization problem.
  • NM ⁇ 1 dimensional space-time snapshot x is expressed as:
  • ⁇ t is the target complex gain
  • Spatial frequency is The space-time steering vector corresponding to the target
  • x u includes a vector of clutter x c , interference x j , and noise x n .
  • the L1 norm-L2 norm mixture minimization objective function is:
  • w p represents the weight vector of the NM ⁇ 1 -dimensional space-time filter calculated by p space-time snapshots
  • J 1 (w p ) represents a function with w p as a variable
  • R p w p represents the l 2 norm of the space-time filter output calculated by p space-time snapshots
  • R p represents the array covariance matrix calculated from p space-time snapshots, ⁇
  • the p 1 space-time snapshot is calculated by the beam-Doppler pattern z p l 1 sparse constraint term,
  • Step S2 solving the weight vector w p of the space-time filter according to the L1 norm-L2 norm hybrid minimization objective function.
  • the L1 norm-L2 norm mixture minimization objective function is first converted into the following formula:
  • ⁇ is the Lagrangian multiplier, Indicates that the number in the braces is the real part
  • equation (4) is a space-time filter weight vector expression
  • the parameter ⁇ is in the following iterative form.
  • the formula (7) is a regularized parameter adaptive alternating iterative algorithm, and ⁇ p (z p ) represents the regularized parameter ⁇ calculated by p space-time snapshots, in order to ensure that the algorithm can converge to the global optimal value,
  • the weight vector w p can be obtained by combining the formula (6) and the formula (7) and using the formula (4).
  • the number of independent and identically distributed training samples is p
  • beam-Dopp is introduced on the basis of the traditional STAP filter design.
  • the sparseness of the directional pattern is established, and the L1 norm-L2 norm mixture minimization objective function is established.
  • the optimal weight vector and regularization parameters are updated by the adaptive alternating iterative algorithm to obtain the weight vector w p of the space-time filter.
  • the method of the invention can improve the clutter suppression level and the target detection capability of the radar system under the condition of limited independent and identically distributed training samples and array errors.
  • the following is a specific embodiment, which provides a space-time adaptive processing STAP method for beam-Doppler pattern sparse constraint provided by the present invention, and JDL, STMB (Space-Time Multiple-Beam), PC, and based on
  • the sparsity-space beamforming method (Sparsity-Aware Beamformer) of the weight vector sparsity is compared to illustrate the beneficial effects obtained by the technical solution provided by the present invention in terms of clutter suppression performance and target detection performance.
  • the carrier frequency is 1.2 GHz
  • the platform speed is 125.
  • Meters per second platform height is 8 kilometers
  • noise to noise ratio (CNR) is 45dB
  • two interference directions are -45 degrees and 60 degrees
  • the dry noise ratio (JNR) is 30dB.
  • the output signal to interference and noise ratio (SINR) loss of the sparse space-time beamforming method of the proposed method and the existing JDL, STMB, PC and weight vector sparsity is compared.
  • the w in the formula (9) is taken as w p , that is, w H is taken as (w p ) H , and the right of the space-time filter is calculated by using the technical solution provided by the present invention.
  • the vector w p is taken into the above formula (9) to obtain the dryness ratio (SINR).
  • the normalized Doppler frequency of the target of interest is 0.25.
  • the present invention exhibits a faster convergence rate and a higher steady state output SINR than several other algorithms.
  • the detection performance of the method and other methods of the present invention that is, the detection probability curve is shown in FIG. 4, in the simulation, the false alarm rate P fa is set to 10 -3 , and the Monte Carlo number obtained by the detection threshold and the detection probability is set to 10/P fa , the target normalized Doppler frequency is 0.25. It can be seen from FIG. 4 that the present invention has the highest detection probability compared with other conventional algorithms, that is, the target detection performance is superior to other algorithms.
  • the method provided by the present invention can obtain a sparse space-time beamforming method superior to JDL, STMB, PC, and weight vector sparsity under the condition of limited independent and identically distributed training samples and array errors. Clutter suppression performance.
  • the present invention also provides a space-time adaptive processing STAP apparatus for beam-Doppler pattern sparse constraint. As shown in FIG. 5, the apparatus includes:
  • the weight vector w p solves the module 2 for solving the weight vector w p of the space-time filter according to the L1 norm-L2 norm mixture minimization objective function.
  • the sparseness of the beam-multiple map is introduced on the basis of the traditional STAP filter design, and the STAP filter design problem is described as an L1 norm-L2 norm hybrid minimization optimization problem, that is, L1 is established.
  • norm norm -L2 mixing minimizing the objective function, and then mixed norm norm -L2 minimize the objective function for solving space-time filter in accordance with the weight vector w p L1.
  • the embodiment of the invention can be applied to the radar clutter suppression field of the motion platform, and the radar system suppression level and the target detection capability are improved under the condition of limited independent and identically distributed training samples and array errors.

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Abstract

一种波束-多普勒方向图稀疏约束的空时自适应处理STAP方法及装置，该方法包括：根据波束-多普勒方向图的稀疏性，联合空时滤波器输出的L2范数和波束-多普勒方向图的L1范数的最小化，建立L1范数-L2范数混合最小化目标函数（S1）；根据L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量w p（S2），其中，上标p为正整数，代表独立同分布训练样本数。该方法参数易设置且计算简单，可以在独立同分布训练样本数有限的条件下，提高雷达系统杂波抑制水平与目标检测能力。

Description

波束-多普勒方向图稀疏约束的STAP方法及装置 技术领域
本发明属于雷达信号处理领域，尤其涉及一种波束-多普勒方向图稀疏约束的STAP方法及装置。
背景技术
相控阵机载雷达中，STAP(Space-Time Adaptive Processing，空时自适应处理)技术是提高目标检测性能的极具优势的一项技术之一。由于在非均匀环境下，很难获得较多的独立同分布训练样本数，那么怎样在独立同分布训练样本数有限的条件下，提高传统空时自适应滤波器的杂波抑制水平与目标检测能力的问题，成为STAP研究主要关注的问题。
针对该问题，学者们提出一些相关方法，如降维(Reduced Dimension)STAP方法(如局域联合处理方法(Joint Domain Localized，JDL))、降秩(Reduced Rank)STAP方法(如主分量法(Principle Components，PC))、基于模型参数化的STAP方法、基于知识的(Knowledge-Aided，KA)STAP方法、基于权矢量稀疏性的稀疏空时波束形成方法、最小-最大STAP方法等等。降维STAP方法利用降低系统自由度的方法，提高了独立同分布训练样本有限下的杂波抑制能力和目标检测性能，但该算法减少了系统自由度，相较于全空时最优系统下的杂波抑制 性能来说，性能有所降低。降秩(Reduced Rank)STAP方法尽管可以实时根据环境变化和样本数据设计滤波器权矢量，也能获得比降维STAP方法更优越的性能，但是降秩STAP方法的性能通常依赖于实际杂波环境中杂波秩估计的准确性，而实际杂波环境中杂波秩的估计精确性仍需更多研究。基于模型参数化的STAP方法利用模型参数法解决了独立同分布训练样本有限的问题，但是该类方法计算复杂度较高，且算法的性能依赖于模型参数选择的合理性。基于知识的STAP方法，在解决在独立同分布训练样本数有限的问题拥有巨大优势，但该类方法的性能依赖于知识的准确性。基于权矢量稀疏性的稀疏空时波束形成方法利用了权矢量稀疏性的先验知识，在独立同分布训练本数有限具有潜在优势，但存在模型失配时，其杂波性能有所降低。最小-最大STAP方法利用迭代最小-最大方法选择天线脉冲对来降低对空时快拍的需求，因此能够在有限快拍下获得较好的杂波抑制能力，但是算法中涉及的迭代最小-最大过程计算复杂度较高，而且当天线脉冲对选择不当时，算法性能严重恶化。
即学者们提出的上述相关方法中，在独立同分布训练样本数有限的条件下，一些算法由于在执行过程中存在一定问题，导致不能很好的提高传统空时自适应滤波器的杂波抑制水平与目标检测能力的问题；另一些算法存在计算复杂度高的问题，或者参数设置困难的问题；因此，需要一种参数易设置且计算简单的算法，能够在独立同分布训练样本数有限的条件下，提高传统空时自适应滤波器的杂波抑制水平与目标检测能力。
发明内容
本发明提供一种波束-多普勒方向图稀疏约束的STAP方法及装置，旨在在独立同分布训练样本数有限的条件下，提供一种参数易设置且计算简单的算法来提高传统空时自适应滤波器的杂波抑制水平与目标检测能力。
本发明提供了一种波束-多普勒方向图稀疏约束的空时自适应处理STAP方法，所述方法包括：
根据波束-多普勒方向图的稀疏性，联合空时滤波器输出的l2范数和波束-多普勒方向图的l1范数的最小化，建立L1范数-L2范数混合最小化目标函数；
根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp；
其中，上标p代表独立同分布训练样本数，p为正整数。
进一步地，所述L1范数-L2范数混合最小化目标函数为：
Figure PCTCN2017087289-appb-000001
其中，wp表示由p个空时快拍计算得到NM×1维空时滤波器的权矢量，J1(wp)表示以wp为变量的函数，(wp)HRpwp表示由p个空时快拍计算得到的空时滤波器输出的l2范数，Rp表示由p个空时快拍计算得到的阵列协方差矩阵，κ||zp||1表示由p个空时快拍计算得到的波束-多普勒方向图zp的l1稀疏约束项，||·||1表示取l1范数，
Figure PCTCN2017087289-appb-000002
表示波束-多普勒空间的波束-多普勒方向图，上标T、H分别表示转置、共轭转置，
Figure PCTCN2017087289-appb-000003
表示多普勒 频率为fd；i、空间频率为fs；j的波束-多普勒方向图，
Figure PCTCN2017087289-appb-000004
为NM×NdNs维矩阵，Nd表示整个多普勒域多普勒频率采样点数，Ns表示整个波束域空间频率采样点数，κ为权衡波束-多普勒方向图稀疏性与滤波器输出l2范数的正则化参数；
Figure PCTCN2017087289-appb-000005
表示取最小值对应的参数wp，s.t.表示约束条件；
NM×1维空时快拍表示为：
x＝αts+xu，
其中，M表示天线阵列的阵元个数，N表示相干脉冲个数，αt为目标复增益；
Figure PCTCN2017087289-appb-000006
为多普勒频率为
Figure PCTCN2017087289-appb-000007
空间频率为
Figure PCTCN2017087289-appb-000008
的目标所对应的空时导向矢量；xu包括杂波xc、干扰xj和噪声xn的矢量。
进一步地，所述根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp，包括：
将所述L1范数-L2范数混合最小化目标函数转化为以下公式：
Figure PCTCN2017087289-appb-000009
其中，λ为拉格朗日乘子，
Figure PCTCN2017087289-appb-000010
表示对大括号里的数取实部；
利用上述公式对(wp)*求导，并令结果为0，然后将结果代入(wp)Hs＝1，即可得到权矢量wp的表达式，根据权矢量wp的表达式求解权矢量wp，其中，wp的表达式为：
Figure PCTCN2017087289-appb-000011
其中，
Figure PCTCN2017087289-appb-000012
其中，(·)*表示取共轭，diag{·}表示以大括号中元素为对角元素构成的对角矩阵，ε表示很小的一个正常数。
进一步地，参数Rp的求解公式为：
Figure PCTCN2017087289-appb-000013
其中，β为遗忘因子，xi表示第i个空时快拍，xp表示第p个空时快拍，上标H分别表示共轭转置，Rp-1表示前p-1个空时快拍计算得到的协方差矩阵。
进一步地，正则化参数κ的求解公式为：
Figure PCTCN2017087289-appb-000014
其中，
Figure PCTCN2017087289-appb-000015
其中，κp(zp)表示由p个空时快拍计算得到的正则化参数κ，
Figure PCTCN2017087289-appb-000016
为常数，且
Figure PCTCN2017087289-appb-000017
本发明还提供了一种波束-多普勒方向图稀疏约束的空时自适应处理STAP装置，所述装置包括：
最小化目标函数建立模块，用于根据波束-多普勒方向图的稀疏性，联合空时滤波器输出的l2范数和波束-多普勒方向图的l1范数的最小化，建立L1范数-L2范数混合最小化目标函数；
权矢量wp求解模块，用于根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp；
其中，上标p代表独立同分布训练样本数，p为正整数。
进一步地，所述L1范数-L2范数混合最小化目标函数为：
Figure PCTCN2017087289-appb-000018
其中，wp表示由p个空时快拍计算得到NM×1维空时滤波器的权矢量，J1(wp)表示以wp为变量的函数，(wp)HRpwp表示由p个空时快拍计算得到的空时滤波器输出的l2范数，Rp表示由p个空时快拍计算得到的阵列协方差矩阵，κ||zp||1表示由p个空时快拍计算得到的波束-多普勒方向图zp的l1稀疏约束项，||·||1表示取l1范数，
Figure PCTCN2017087289-appb-000019
表示波束-多普勒空间的波束-多普勒方向图，上标T、H分别表示转置、共轭转置，
Figure PCTCN2017087289-appb-000020
表示多普勒频率为fd；i、空间频率为fs；j的波束-多普勒方向图，
Figure PCTCN2017087289-appb-000021
为NM×NdNs维矩阵，Nd表示整个多普勒域多普勒频率采样点数，Ns表示整个波束域空间频率采样点数，κ为权衡波束-多普勒方向图稀疏性与滤波器输出l2范数的正则化参数；
Figure PCTCN2017087289-appb-000022
表示取最小值对应的参数wp，s.t.表示约束条件；
NM×1维空时快拍表示为：
x＝αts+xu，
其中，M表示天线阵列的阵元个数，N表示相干脉冲个数，αt为目标复增 益；
Figure PCTCN2017087289-appb-000023
为多普勒频率为
Figure PCTCN2017087289-appb-000024
空间频率为
Figure PCTCN2017087289-appb-000025
的目标所对应的空时导向矢量；xu包括杂波xc、干扰xj和噪声xn的矢量。
进一步地，所述权矢量wp求解模块，具体用于将所述L1范数-L2范数混合最小化目标函数转化为以下公式：
Figure PCTCN2017087289-appb-000026
其中，λ为拉格朗日乘子，
Figure PCTCN2017087289-appb-000027
表示对大括号里的数取实部；
并利用上述公式对(wp)*求导，并令结果为0，然后将结果代入(wp)Hs＝1，即可得到权矢量wp的表达式，根据权矢量wp的表达式求解权矢量wp，其中，wp的表达式为：
Figure PCTCN2017087289-appb-000028
其中，
Figure PCTCN2017087289-appb-000029
其中，(·)*表示取共轭，diag{·}表示以大括号中元素为对角元素构成的对角矩阵，ε表示很小的一个正常数。
进一步地，参数Rp的求解公式为：
Figure PCTCN2017087289-appb-000030
其中，β为遗忘因子，xi表示第i个空时快拍，xp表示第p个空时快拍，上标H分别表示共轭转置，Rp-1表示前p-1个空时快拍计算得到的协方差矩阵。
进一步地，正则化参数κ的求解公式为：
Figure PCTCN2017087289-appb-000031
其中，
Figure PCTCN2017087289-appb-000032
其中，κp(zp)表示由p个空时快拍计算得到的正则化参数κ，
Figure PCTCN2017087289-appb-000033
为常数，且
Figure PCTCN2017087289-appb-000034
本发明与现有技术相比，有益效果在于：本发明提供的一种波束-多普勒方向图稀疏约束的STAP方法及装置，在独立同分布训练样本数为p的情况下，通过在传统STAP滤波器设计的基础上引入波束-多普图方向图的稀疏性，将STAP滤波器设计问题描述为L1范数-L2范数混合最小化优化问题，联合空时滤波器输出的l2范数和波束-多普勒方向图的l1范数的最小化，建立L1范数-L2范数混合最小化目标函数，并根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp，从而求解了上述最小化优化问题；本发明提供的方法参数易设置且计算简单，可以在独立同分布训练样本数有限的条件下，提高雷达系统杂波抑制水平与目标检测能力。
附图说明
图1是本发明实施例提供的一种波束-多普勒方向图稀疏约束的空时自适应处理STAP方法的流程示意图；
图2是本发明实施例提供的SINR损失与训练样本数关系的示意图；
图3是本发明实施例提供的SINR损失与目标多普勒频率关系的示意图；
图4是本发明实施例提供的检测概率与目标输入信噪比(SNR)的关系的示意图；
图5是本发明实施例提供的一种波束-多普勒方向图稀疏约束的空时自适应处理STAP装置的模块示意图。
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。
本发明的主要实现思想为：在独立同分布训练样本数为p的情况下，通过在传统STAP滤波器设计的基础上引入波束-多普图方向图的稀疏性，将STAP滤波器设计问题描述为L1范数-L2范数混合最小化优化问题，联合空时滤波器输出的l2范数和波束-多普勒方向图的l1范数的最小化，建立L1范数-L2范数混合最小化目标函数，并根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp，从而求解了上述最小化优化问题。
下面具体介绍这种波束-多普勒方向图稀疏约束的空时自适应处理STAP方法，如图1所示，所述方法包括：
步骤S1，根据波束-多普勒方向图的稀疏性，联合空时滤波器输出的l2范 数和波束-多普勒方向图的l1范数的最小化，建立L1范数-L2范数混合最小化目标函数；
具体地，波束-多普勒方向的稀疏性是指波束-多普勒方向图在目标方向形成高增益，而在除目标方向以外的其它方向形成非常小的增益，即一个矢量中大多数分量的值较小，只有几个分量的值较大，即说信号具有稀疏性。本发明实施例是在传统STAP设计的输出功率最小化问题上，假设空时快拍个数为p(p为正整数)，利用空时滤波器权矢量形成的波束-多普勒方向图的稀疏性，联合空时滤波器输出功率(空时滤波器输出功率的数学意义是l2范数)和波束-多普勒方向图的l1范数最小化，得目标优化问题。
具体地，关于空时快拍的表示方法解释如下：
假设一脉冲多普勒雷达，其天线阵列为均匀线阵，包含M个阵元，一个相干处理时间内以恒定脉冲重复频率(PRF)fr发送N个相干脉冲，感兴趣距离单元只有一个目标，则NM×1维空时快拍x表示为：
x＝αts+xu     (1)
其中，αt为目标复增益；
Figure PCTCN2017087289-appb-000035
为多普勒频率为
Figure PCTCN2017087289-appb-000036
空间频率为
Figure PCTCN2017087289-appb-000037
的目标所对应的空时导向矢量；xu包括杂波xc、干扰xj和噪声xn的矢量。
具体地，所述L1范数-L2范数混合最小化目标函数为：
Figure PCTCN2017087289-appb-000038
其中，wp表示由p个空时快拍计算得到NM×1维空时滤波器的权矢量，J1(wp)表示以wp为变量的函数，(wp)HRpwp表示由p个空时快拍计算得到的空时滤波器输出的l2范数，Rp表示由p个空时快拍计算得到的阵列协方差矩阵，κ||zp||1表示由p个空时快拍计算得到的波束-多普勒方向图zp的l1稀疏约束项，||·||1表示取l1范数，
Figure PCTCN2017087289-appb-000039
表示波束-多普勒空间的波束-多普勒方向图，其中，上标T、H分别表示转置、共轭转置，
Figure PCTCN2017087289-appb-000040
表示多普勒频率为fd；i、空间频率为fs；j的波束-多普勒方向图，v(.，.)表示空时导向矢量，fd；i的取值范围是-0.5到0.5，fs；j的取值范围是-0.5到0.5，
Figure PCTCN2017087289-appb-000041
为NM×NdNs维矩阵，Nd表示整个多普勒域多普勒频率采样点数，Ns表示整个波束域空间频率采样点数，κ为权衡波束-多普勒方向图稀疏性与滤波器输出l2范数的正则化参数；
Figure PCTCN2017087289-appb-000042
表示取最小值对应的参数wp，s.t.表示约束条件。
步骤S2，根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp。
具体地，先将所述L1范数-L2范数混合最小化目标函数转化为以下公式：
Figure PCTCN2017087289-appb-000043
其中，λ为拉格朗日乘子，
Figure PCTCN2017087289-appb-000044
表示对大括号里的数取实部；
然后，为求解式(3)中的权矢量wp，利用上述公式(3)对(wp)*求导，并令结果为0，然后将结果代入(wp)Hs＝1，即可得到权矢量wp的表达式，根据 权矢量wp的表达式即可求解权矢量w，其中，wp的表达式为：
Figure PCTCN2017087289-appb-000045
其中，公式(4)为空时滤波器权矢量表达式；
其中，
Figure PCTCN2017087289-appb-000046
其中，(·)*表示取共轭，diag{·}表示以大括号中元素为对角元素构成的对角矩阵，ε表示很小的一个正常数。
具体地，对于公式(4)中的Rp，按以下迭代方法进行求解：
Figure PCTCN2017087289-appb-000047
其中，β为遗忘因子，p个空时快拍表示为X＝[x1，x2，…，xp]，xi表示第i个空时快拍，i＝1，2，…，p，xp表示第p个空时快拍，上标H分别表示共轭转置，Rp-1表示前p-1个空时快拍计算得到的协方差矩阵。
具体地，为进一步求解公式(4)中的wp，将参数κ采用如下迭代形式
Figure PCTCN2017087289-appb-000048
其中，公式(7)为正则化参数自适应交替迭代算法，κp(zp)表示由p个空时快拍计算得到的正则化参数κ，为保证算法能收敛到全局最优值，令
Figure PCTCN2017087289-appb-000049
其中，
Figure PCTCN2017087289-appb-000050
为常数，且
Figure PCTCN2017087289-appb-000051
即结合公式(6)和公式(7)，并利用公式(4)即可求得权矢量wp。
本发明实施例提出的一种波束-多普勒方向图稀疏约束的STAP方法，在独立同分布训练样本数为p的情况下，首先通过在传统STAP滤波器设计的基础上引入波束-多普勒方向图的稀疏性，并建立L1范数-L2范数混合最小化目标函数，然后利用自适应交替迭代算法更新最优权矢量和正则化参数，求解得到空时滤波器的权矢量wp。本发明所提方法能在有限独立同分布训练样本数和存在阵列误差的条件下，提高雷达系统杂波抑制水平与目标检测能力。
下面举一具体实施例，将本发明提供的波束-多普勒方向图稀疏约束的空时自适应处理STAP方法与JDL、STMB(Space-Time Multiple-Beam，空时多波束)、PC以及基于权矢量稀疏性的稀疏空时波束形成方法(Sparsity-Aware Beamformer)进行对比，来说明本发明提供的技术方案在杂波抑制性能和目标检测性能方面取得的有益效果。
考虑正侧视均均线阵机载雷达平台，阵元数为M＝12，一个相干处理时间内发送脉冲数N＝12，载波频率为1.2GHz，脉冲重复频率fr＝2kHz，平台速度为125米每秒，平台高度为8千米，杂噪比(CNR)为45dB，两个干扰方向为-45度和60度，干噪比(JNR)为30dB，考虑存在阵列幅相误差：阵列幅度和相位误差满足零均值高斯分布，幅度误差和相位误差的方差分别为0.05，0.05*π/2。各算法参数设置如下：JDL算法中，选择3个多普勒通道和3个波 束通道；STMB算法中，选择8个多普勒频率通道和3个波束通道；PC算法中，大特征值个数设置为50；本发明技术所提出算法中，w0＝s，β＝0.9998，ε＝10-6，
Figure PCTCN2017087289-appb-000052
关于杂波抑制性能：
为考察所提算法的杂波抑制性能，比较本发明所提方法与现有JDL、STMB、PC及权矢量稀疏性的稀疏空时波束形成方法的输出信干噪比(SINR)损失，通常可定义为
Figure PCTCN2017087289-appb-000053
需要说明的是，对于本发明所提方法，是将公式(9)中的w取wp，即wH取(wp)H，利用本发明提供的技术方案计算出空时滤波器的权矢量wp，并带入上述公式(9)，来得到性干燥比(SINR)。
在图2中，设感兴趣目标的归一化多普勒频率为0.25。由图2可以看出，相比其他几种算法，本发明表现出更快的收敛速度和更高的稳定状态输出SINR。
在图3中，设各算法的训练样本数即空时快拍个数均为50。由图3可以看出，当归一化多普勒频率小于等于0.1时，所提算法的输出SINR略小于JDL算法，但是在其他多普勒频率值上，所提算法输出SINR都明显优于其他算法。
关于检测性能：
本发明所提方法与其他方法的检测性能，即检测概率曲线如图4所示，仿真中，虚警率Pfa设为10-3，检测门限和检测概率获得的蒙特卡洛次数均设为10/Pfa，感兴趣目标归一化多普勒频率为0.25。由图4可得：本发明相比其他传统算法有最高的检测概率，即目标检测性能优于其他算法。
由以上实施例可得，本发明所提供的方法在有限独立同分布训练样本数和存在阵列误差的条件下，能获得优于JDL、STMB、PC以及权矢量稀疏性的稀疏空时波束形成方法的杂波抑制性能。
本发明还提供了一种波束-多普勒方向图稀疏约束的空时自适应处理STAP装置，如图5所示，所述装置包括：
最小化目标函数建立模块1，用于根据波束-多普勒方向图的稀疏性，联合空时滤波器输出的l2范数和波束-多普勒方向图的l1范数的最小化，建立L1范数-L2范数混合最小化目标函数；
权矢量wp求解模块2，用于根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp。
本发明实施例通过在传统STAP滤波器设计的基础上引入波束-多普图方向图的稀疏性，将STAP滤波器设计问题描述为L1范数-L2范数混合最小化优化问题，即建立L1范数-L2范数混合最小化目标函数，然后根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp。本发明实施例可以应用于运动平台雷达杂波抑制领域，在有限独立同分布训练样本数和存在阵列误差 的条件下，提高雷达系统杂波抑制水平与目标检测能力。
以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。

Claims (10)

  1. 一种波束-多普勒方向图稀疏约束的空时自适应处理STAP方法，其特征在于，所述方法包括：
    根据波束-多普勒方向图的稀疏性，联合空时滤波器输出的l2范数和波束-多普勒方向图的l1范数的最小化，建立L1范数-L2范数混合最小化目标函数；
    根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp；
    其中，上标p代表独立同分布训练样本数，p为正整数。
  2. 如权利要求1所述的STAP方法，其特征在于，所述L1范数-L2范数混合最小化目标函数为：
    Figure PCTCN2017087289-appb-100001
    s.t.(wp)Hs＝1.
    其中，wp表示由p个空时快拍计算得到NM×1维空时滤波器的权矢量，J1(wp)表示以wp为变量的函数，(wp)HRpwp表示由p个空时快拍计算得到的空时滤波器输出的l2范数，Rp表示由p个空时快拍计算得到的阵列协方差矩阵，κ||zp||1表示由p个空时快拍计算得到的波束-多普勒方向图zp的l1稀疏约束项，||·||1表示取l1范数，
    Figure PCTCN2017087289-appb-100002
    表示波束-多普勒空间的波束-多普勒方向图，上标T、H分别表示转置、共轭转置，
    Figure PCTCN2017087289-appb-100003
    表示多普勒频率为fd；i、空间频率为fs；j的波束-多普勒方向图，
    Figure PCTCN2017087289-appb-100004
    为 NM×NdNs维矩阵，Nd表示整个多普勒域多普勒频率采样点数，Ns表示整个波束域空间频率采样点数，κ为权衡波束-多普勒方向图稀疏性与滤波器输出l2范数的正则化参数；
    Figure PCTCN2017087289-appb-100005
    表示取最小值对应的参数wp，s.t.表示约束条件；
    NM×1维空时快拍表示为：
    x＝αts+xu，
    其中，M表示天线阵列的阵元个数，N表示相干脉冲个数，αt为目标复增益；
    Figure PCTCN2017087289-appb-100006
    为多普勒频率为
    Figure PCTCN2017087289-appb-100007
    空间频率为
    Figure PCTCN2017087289-appb-100008
    的目标所对应的空时导向矢量；xu包括杂波xc、干扰xj和噪声xn的矢量。
  3. 如权利要求2所述的STAP方法，其特征在于，所述根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp，包括：
    将所述L1范数-L2范数混合最小化目标函数转化为以下公式：
    Figure PCTCN2017087289-appb-100009
    其中，λ为拉格朗日乘子，
    Figure PCTCN2017087289-appb-100010
    表示对大括号里的数取实部；
    利用上述公式对(wp)*求导，并令结果为0，然后将结果代入(wp)Hs＝1，即可得到权矢量wp的表达式，根据权矢量wp的表达式求解权矢量wp，其中，wp的表达式为：
    Figure PCTCN2017087289-appb-100011
    其中，
    Figure PCTCN2017087289-appb-100012
    其中，(·)*表示取共轭，diag{·}表示以大括号中元素为对角元素构成的对角矩阵，ε表示很小的一个正常数。
  4. 如权利要求3所述的STAP方法，其特征在于，参数Rp的求解公式为：
    Figure PCTCN2017087289-appb-100013
    其中，β为遗忘因子，xi表示第i个空时快拍，xp表示第p个空时快拍，上标H分别表示共轭转置，Rp-1表示前p-1个空时快拍计算得到的协方差矩阵。
  5. 如权利要求4所述的STAP方法，其特征在于，正则化参数κ的求解公式为：
    Figure PCTCN2017087289-appb-100014
    其中，
    Figure PCTCN2017087289-appb-100015
    其中，κp(zp)表示由p个空时快拍计算得到的正则化参数κ，
    Figure PCTCN2017087289-appb-100016
    为常数，且
    Figure PCTCN2017087289-appb-100017
  6. 一种波束-多普勒方向图稀疏约束的空时自适应处理STAP装置，其特征在于，所述装置包括：
    最小化目标函数建立模块，用于根据波束-多普勒方向图的稀疏性，联合空时滤波器输出的l2范数和波束-多普勒方向图的l1范数的最小化，建立L1范数-L2范数混合最小化目标函数；
    权矢量wp求解模块，用于根据所述L1范数-L2范数混合最小化目标函数求解空时滤波器的权矢量wp；
    其中，上标p代表独立同分布训练样本数，p为正整数。
  7. 如权利要求6所述的STAP装置，其特征在于，所述L1范数-L2范数混合最小化目标函数为：
    Figure PCTCN2017087289-appb-100018
    s.t.(wp)Hs＝1.
    其中，wp表示由p个空时快拍计算得到NM×1维空时滤波器的权矢量，J1(wp)表示以wp为变量的函数，(wp)HRpwp表示由p个空时快拍计算得到的空时滤波器输出的l2范数，Rp表示由p个空时快拍计算得到的阵列协方差矩阵，κ||zp||1表示由p个空时快拍计算得到的波束-多普勒方向图zp的l1稀疏约束项，||·||1表示取l1范数，
    Figure PCTCN2017087289-appb-100019
    表示波束-多普勒空间的波束-多普勒方向图，上标T、H分别表示转置、共轭转置，
    Figure PCTCN2017087289-appb-100020
    表示多普勒频率为fd；i、空间频率为fs；j的波束-多普勒方向图，
    Figure PCTCN2017087289-appb-100021
    为NM×NdNs维矩阵，Nd表示整个多普勒域多普勒频率采样点数，Ns表示整个波束域空间频率采样点数，κ为权衡波束-多普勒方向图稀疏性与滤波器输出l2范数的正则化参数；
    Figure PCTCN2017087289-appb-100022
    表示取最小值对应的参数wp，s.t.表示约束条件；
    NM×1维空时快拍表示为：
    x＝αts+xu，
    其中，M表示天线阵列的阵元个数，N表示相干脉冲个数，αt为目标复增益；
    Figure PCTCN2017087289-appb-100023
    为多普勒频率为
    Figure PCTCN2017087289-appb-100024
    空间频率为
    Figure PCTCN2017087289-appb-100025
    的目标所对应的空时导向矢量；xu包括杂波xc、干扰xj和噪声xn的矢量。
  8. 如权利要求7所述的STAP装置，其特征在于，所述权矢量wp求解模块，具体用于将所述L1范数-L2范数混合最小化目标函数转化为以下公式：
    Figure PCTCN2017087289-appb-100026
    其中，λ为拉格朗日乘子，
    Figure PCTCN2017087289-appb-100027
    表示对大括号里的数取实部；
    并利用上述公式对(wp)*求导，并令结果为0，然后将结果代入(wp)Hs＝1，即可得到权矢量wp的表达式，根据权矢量wp的表达式求解权矢量wp，其中，wp的表达式为：
    Figure PCTCN2017087289-appb-100028
    其中，
    Figure PCTCN2017087289-appb-100029
    其中，(·)*表示取共轭，diag{·}表示以大括号中元素为对角元素构成的对角矩阵，ε表示很小的一个正常数。
  9. 如权利要求8所述的STAP装置，其特征在于，参数Rp的求解公式为：
    Figure PCTCN2017087289-appb-100030
    其中，β为遗忘因子，xi表示第i个空时快拍，xp表示第p个空时快拍，上 标H分别表示共轭转置，Rp-1表示前p-1个空时快拍计算得到的协方差矩阵。
  10. 如权利要求9所述的STAP装置，其特征在于，正则化参数κ的求解公式为：
    Figure PCTCN2017087289-appb-100031
    其中，
    Figure PCTCN2017087289-appb-100032
    其中，κp(zp)表示由p个空时快拍计算得到的正则化参数κ，
    Figure PCTCN2017087289-appb-100033
    为常数，且
    Figure PCTCN2017087289-appb-100034
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